Answer:
-2200 N
Explanation:
Here we can use the impulse theorem, which states that the impulse exerted on Sarah (product of force and duration of collision) is equal to Sarah's change in momentum:
[tex]I=\Delta p\\F \Delta t = m \Delta v[/tex]
where
F is the average force
[tex]\Delta t[/tex] is the duration of the collision
m is the mass
[tex]\Delta v[/tex] is the change in velocity
In this problem:
m = 55 kg
[tex]\Delta v = 0-20 = -20 m/s[/tex]
[tex]\Delta t = 0.5 s[/tex]
Solving the formula, we find the force exerted by the seatbelt on Sarah:
[tex]F=\frac{m\Delta v}{\Delta t}=\frac{(55)(-20)}{0.5}=-2200 N[/tex]
And the negative sign means the direction is opposite to that of Sarah's initial motion.
